1. **State the problem:** We need to put the fractions $\frac{7}{10}$, $\frac{8}{15}$, and $\frac{3}{5}$ in ascending order. 2. **Find a common denominator:** To compare fractions, convert them to have the same denominator. The denominators are 10, 15, and 5. 3. **Calculate the least common denominator (LCD):** $$\text{LCD} = \text{lcm}(10, 15, 5)$$ Prime factors: - 10 = $2 \times 5$ - 15 = $3 \times 5$ - 5 = $5$ The LCD must include $2$, $3$, and $5$, so: $$\text{LCD} = 2 \times 3 \times 5 = 30$$ 4. **Convert each fraction to have denominator 30:** $$\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}$$ $$\frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}$$ $$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$$ 5. **Compare the numerators:** $$16 < 18 < 21$$ 6. **Write the fractions in ascending order:** $$\frac{8}{15} < \frac{3}{5} < \frac{7}{10}$$